TK carburetors are made by Teikei Co, a Japanese manufacturer.
As I understand it, you are saying the engine will start easily, and will continue to idle: it does not run out of fuel while idling. However when you open the throttle, it runs out of fuel.
The next question is, if you open the throttle fully, will it run up to full speed briefly, then starve out? If so, the problem is insufficient fuel delivery from the fuel pump. If it just goes lean whenever it revs up, this would mean the main jet or its fuel path is obstructed. So, the key question is whether there is a time delay between opening the throttle and starving out, or it always starves out at high speed, and it happens instantly.
Once that is clear, it will be evident whether you should be looking at the fuel pump or the fuel passages. If it is a pump problem, you should start with the fine mesh fuel filter in the bottom of the pump chamber. If it isn't that, you need to look closely at the pump diaphragm itself.
If it is a fuel flow problem, not a pump issue, you will have to strip the carburetor and clean its passages.
Here is a workshop manual for a Shindaiwa trimmer that uses a TK carburetor, which I think is fairly similar to yours:
http://golftechs.us/Manuals/shin%20trimmers.pdf
